Burkhard Eden

The super-correlator/super-amplitude duality: Part II

We extend the recently discovered duality between MHV amplitudes and the light-cone limit of correlation functions of a particular type of local scalar operators to generic nonMHV amplitudes in planar N = 4 SYM theory. We consider the natural generalization of the bosonic correlators to super-correlators of stress-tensor multiplets and show, in a number of examples, that their light-cone limit exactly reproduces the square of the matching super-amplitudes. Our correlators are computed at Born level. If all of their points form a light-like polygon, the correlator is dual to the tree-level amplitude. If a subset of points are not on the polygon but are integrated over, they become Lagrangian insertions generating the loop corrections to the correlator. In this case the duality with amplitudes holds at the level of the integrand. We build up the superspace formalism needed to formulate the duality and present the explicit example of the n−point NMHV tree amplitude as the dual of the lowest nilpotent level in the correlator. Unité de Recherche Associée au CNRS URA 2306 Laboratoire d’Annecy-le-Vieux de Physique Théorique, UMR 5108

Bootstrapping correlation functions in N=4 SYM

A bstractWe describe a new approach to computing the chiral part of correlation functions of stress-tensor supermultiplets in N=4

Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM

\mathcal{N}=4

Leading singularities and off-shell conformal integrals

SYM that relies on symmetries, analytic properties and the structure of the OPE only. We demonstrate that the correlation functions are given by a linear combination of chiral N=4

Three-point functions in \( \mathcal{N}=4 \) SYM: the hexagon proposal at three loops

\mathcal{N}=4

Local integrands for the five-point amplitude in planar N=4 SYM up to five loops.

superconformal invariants accompanied by coefficient functions depending on the space-time coordinates only. We present the explicit construction of these invariants and show that the six-point correlation function is fixed in the Born approximation up to four constant coefficients by its symmetries. In addition, the known asymptotic structure of the correlation function in the light-like limit fixes unambiguously these coefficients up to an overall normalization. We demonstrate that the same approach can be applied to obtain a representation for the six-point NMHV amplitude that is free from any auxiliary gauge fixing parameters, does not involve spurious poles and manifests half of the dual superconformal symmetry.